Determination of the Boltzmann Constant by Means of Precision Measurements ofH2O18Line Shapes at1.39 

Abstract

We report on a new implementation of Doppler broadening thermometry based on precision absorption spectroscopy by means of a pair of offset-frequency locked extended-cavity diode lasers at 1.39 μm. The method consists in the highly accurate observation of the shape of the 4(4,1)→4(4,0) line of the H2(18)O ν1+ν3 band, in a water vapor sample at thermodynamic equilibrium. A sophisticated and extremely refined spectral analysis procedure is adopted for the retrieval of the Doppler width as a function of the gas pressure, taking into account the Dicke narrowing effect, the speed dependence of relaxation rates, and the physical correlation between velocity-changing and dephasing collisions. A spectroscopic determination of the Boltzmann constant with a combined (type A and type B) uncertainty of 24 parts over 10(6) is reported. This is the best result obtained so far by means of an optical method. Our determination is in agreement with the recommended CODATA value.

Velocity-changing collisions in pure H2 and H2-Ar mixture

“…These results are crucial from the point of view of recent very rapid developments of ultra-accurate spectroscopic measurements, where effective accuracy is no longer limited by experimental imperfections, but by the use of wrong line-shape models. 4,5,25 We showed that the BB model properly describes the velocity-changing collisions for H 2 -H 2 and H 2 -Ar. We did it by relating the results obtained from the BB model to those from ab initio CMDS.…”

“…For other systems, well controlled quantification of these systematic errors will allow to increase the accuracy in many, recently rapidly developing, fields of optical metrology like spectroscopic determination of Boltzmann constant, where at the moment the main contribution to the error budget comes from oversimplified treatment of the spectral line shape. 4 The effective frequency of velocity-changing collisions…”

“…Clearly, the use of realistic description of collisions in line shape calculations is crucial for different applications such as the spectroscopic determination of the Boltzmann constant, 4,5,46,86 testing quantum treatment of molecules with high precision (in particular, line intensities) 49 or search for new fundamental physical effects. 87,88 Comparing the descriptions of the velocity-changing collisions given by various models (see Sec.…”

“…These results allow to remove the limitations on accuracy of physical quantities obtained from spectra analysis and therefore they are important for optical metrology based on molecular spectroscopy like Doppler-width thermometry and Boltzmann constant determination, 4,5,46 atmosphere monitoring, 47,48 or transition position and intensity determination for fundamental studies. 49 …”

“…One can note the tremendous increase in accuracy and precision of line shape measurement in the Doppler limited spectroscopy. Let us only mention ultra high sensitivity 1,2 approaching 10 −13 cm −1 , measurement of transition frequencies 3 with accuracy at the kHz level, determination of Boltzmann constant from Doppler line broadening 4,5 with accuracy approaching 10 −5 and ultra high signal-to-noise ratio 6 beyond 10 5 level. Such progress is accompanied by the development of line shape theory of isolated spectral line.…”